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<FONT color="green">001</FONT>    /*<a name="line.1"></a>
<FONT color="green">002</FONT>     * Licensed to the Apache Software Foundation (ASF) under one or more<a name="line.2"></a>
<FONT color="green">003</FONT>     * contributor license agreements.  See the NOTICE file distributed with<a name="line.3"></a>
<FONT color="green">004</FONT>     * this work for additional information regarding copyright ownership.<a name="line.4"></a>
<FONT color="green">005</FONT>     * The ASF licenses this file to You under the Apache License, Version 2.0<a name="line.5"></a>
<FONT color="green">006</FONT>     * (the "License"); you may not use this file except in compliance with<a name="line.6"></a>
<FONT color="green">007</FONT>     * the License.  You may obtain a copy of the License at<a name="line.7"></a>
<FONT color="green">008</FONT>     *<a name="line.8"></a>
<FONT color="green">009</FONT>     *      http://www.apache.org/licenses/LICENSE-2.0<a name="line.9"></a>
<FONT color="green">010</FONT>     *<a name="line.10"></a>
<FONT color="green">011</FONT>     * Unless required by applicable law or agreed to in writing, software<a name="line.11"></a>
<FONT color="green">012</FONT>     * distributed under the License is distributed on an "AS IS" BASIS,<a name="line.12"></a>
<FONT color="green">013</FONT>     * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.<a name="line.13"></a>
<FONT color="green">014</FONT>     * See the License for the specific language governing permissions and<a name="line.14"></a>
<FONT color="green">015</FONT>     * limitations under the License.<a name="line.15"></a>
<FONT color="green">016</FONT>     */<a name="line.16"></a>
<FONT color="green">017</FONT>    package org.apache.commons.math3.analysis.interpolation;<a name="line.17"></a>
<FONT color="green">018</FONT>    <a name="line.18"></a>
<FONT color="green">019</FONT>    import org.apache.commons.math3.exception.DimensionMismatchException;<a name="line.19"></a>
<FONT color="green">020</FONT>    import org.apache.commons.math3.exception.util.LocalizedFormats;<a name="line.20"></a>
<FONT color="green">021</FONT>    import org.apache.commons.math3.exception.NumberIsTooSmallException;<a name="line.21"></a>
<FONT color="green">022</FONT>    import org.apache.commons.math3.exception.NonMonotonicSequenceException;<a name="line.22"></a>
<FONT color="green">023</FONT>    import org.apache.commons.math3.analysis.polynomials.PolynomialFunction;<a name="line.23"></a>
<FONT color="green">024</FONT>    import org.apache.commons.math3.analysis.polynomials.PolynomialSplineFunction;<a name="line.24"></a>
<FONT color="green">025</FONT>    import org.apache.commons.math3.util.MathArrays;<a name="line.25"></a>
<FONT color="green">026</FONT>    <a name="line.26"></a>
<FONT color="green">027</FONT>    /**<a name="line.27"></a>
<FONT color="green">028</FONT>     * Computes a natural (also known as "free", "unclamped") cubic spline interpolation for the data set.<a name="line.28"></a>
<FONT color="green">029</FONT>     * &lt;p&gt;<a name="line.29"></a>
<FONT color="green">030</FONT>     * The {@link #interpolate(double[], double[])} method returns a {@link PolynomialSplineFunction}<a name="line.30"></a>
<FONT color="green">031</FONT>     * consisting of n cubic polynomials, defined over the subintervals determined by the x values,<a name="line.31"></a>
<FONT color="green">032</FONT>     * x[0] &lt; x[i] ... &lt; x[n].  The x values are referred to as "knot points."&lt;/p&gt;<a name="line.32"></a>
<FONT color="green">033</FONT>     * &lt;p&gt;<a name="line.33"></a>
<FONT color="green">034</FONT>     * The value of the PolynomialSplineFunction at a point x that is greater than or equal to the smallest<a name="line.34"></a>
<FONT color="green">035</FONT>     * knot point and strictly less than the largest knot point is computed by finding the subinterval to which<a name="line.35"></a>
<FONT color="green">036</FONT>     * x belongs and computing the value of the corresponding polynomial at &lt;code&gt;x - x[i] &lt;/code&gt; where<a name="line.36"></a>
<FONT color="green">037</FONT>     * &lt;code&gt;i&lt;/code&gt; is the index of the subinterval.  See {@link PolynomialSplineFunction} for more details.<a name="line.37"></a>
<FONT color="green">038</FONT>     * &lt;/p&gt;<a name="line.38"></a>
<FONT color="green">039</FONT>     * &lt;p&gt;<a name="line.39"></a>
<FONT color="green">040</FONT>     * The interpolating polynomials satisfy: &lt;ol&gt;<a name="line.40"></a>
<FONT color="green">041</FONT>     * &lt;li&gt;The value of the PolynomialSplineFunction at each of the input x values equals the<a name="line.41"></a>
<FONT color="green">042</FONT>     *  corresponding y value.&lt;/li&gt;<a name="line.42"></a>
<FONT color="green">043</FONT>     * &lt;li&gt;Adjacent polynomials are equal through two derivatives at the knot points (i.e., adjacent polynomials<a name="line.43"></a>
<FONT color="green">044</FONT>     *  "match up" at the knot points, as do their first and second derivatives).&lt;/li&gt;<a name="line.44"></a>
<FONT color="green">045</FONT>     * &lt;/ol&gt;&lt;/p&gt;<a name="line.45"></a>
<FONT color="green">046</FONT>     * &lt;p&gt;<a name="line.46"></a>
<FONT color="green">047</FONT>     * The cubic spline interpolation algorithm implemented is as described in R.L. Burden, J.D. Faires,<a name="line.47"></a>
<FONT color="green">048</FONT>     * &lt;u&gt;Numerical Analysis&lt;/u&gt;, 4th Ed., 1989, PWS-Kent, ISBN 0-53491-585-X, pp 126-131.<a name="line.48"></a>
<FONT color="green">049</FONT>     * &lt;/p&gt;<a name="line.49"></a>
<FONT color="green">050</FONT>     *<a name="line.50"></a>
<FONT color="green">051</FONT>     * @version $Id: SplineInterpolator.java 1379905 2012-09-01 23:56:50Z erans $<a name="line.51"></a>
<FONT color="green">052</FONT>     */<a name="line.52"></a>
<FONT color="green">053</FONT>    public class SplineInterpolator implements UnivariateInterpolator {<a name="line.53"></a>
<FONT color="green">054</FONT>        /**<a name="line.54"></a>
<FONT color="green">055</FONT>         * Computes an interpolating function for the data set.<a name="line.55"></a>
<FONT color="green">056</FONT>         * @param x the arguments for the interpolation points<a name="line.56"></a>
<FONT color="green">057</FONT>         * @param y the values for the interpolation points<a name="line.57"></a>
<FONT color="green">058</FONT>         * @return a function which interpolates the data set<a name="line.58"></a>
<FONT color="green">059</FONT>         * @throws DimensionMismatchException if {@code x} and {@code y}<a name="line.59"></a>
<FONT color="green">060</FONT>         * have different sizes.<a name="line.60"></a>
<FONT color="green">061</FONT>         * @throws NonMonotonicSequenceException if {@code x} is not sorted in<a name="line.61"></a>
<FONT color="green">062</FONT>         * strict increasing order.<a name="line.62"></a>
<FONT color="green">063</FONT>         * @throws NumberIsTooSmallException if the size of {@code x} is smaller<a name="line.63"></a>
<FONT color="green">064</FONT>         * than 3.<a name="line.64"></a>
<FONT color="green">065</FONT>         */<a name="line.65"></a>
<FONT color="green">066</FONT>        public PolynomialSplineFunction interpolate(double x[], double y[])<a name="line.66"></a>
<FONT color="green">067</FONT>            throws DimensionMismatchException,<a name="line.67"></a>
<FONT color="green">068</FONT>                   NumberIsTooSmallException,<a name="line.68"></a>
<FONT color="green">069</FONT>                   NonMonotonicSequenceException {<a name="line.69"></a>
<FONT color="green">070</FONT>            if (x.length != y.length) {<a name="line.70"></a>
<FONT color="green">071</FONT>                throw new DimensionMismatchException(x.length, y.length);<a name="line.71"></a>
<FONT color="green">072</FONT>            }<a name="line.72"></a>
<FONT color="green">073</FONT>    <a name="line.73"></a>
<FONT color="green">074</FONT>            if (x.length &lt; 3) {<a name="line.74"></a>
<FONT color="green">075</FONT>                throw new NumberIsTooSmallException(LocalizedFormats.NUMBER_OF_POINTS,<a name="line.75"></a>
<FONT color="green">076</FONT>                                                    x.length, 3, true);<a name="line.76"></a>
<FONT color="green">077</FONT>            }<a name="line.77"></a>
<FONT color="green">078</FONT>    <a name="line.78"></a>
<FONT color="green">079</FONT>            // Number of intervals.  The number of data points is n + 1.<a name="line.79"></a>
<FONT color="green">080</FONT>            final int n = x.length - 1;<a name="line.80"></a>
<FONT color="green">081</FONT>    <a name="line.81"></a>
<FONT color="green">082</FONT>            MathArrays.checkOrder(x);<a name="line.82"></a>
<FONT color="green">083</FONT>    <a name="line.83"></a>
<FONT color="green">084</FONT>            // Differences between knot points<a name="line.84"></a>
<FONT color="green">085</FONT>            final double h[] = new double[n];<a name="line.85"></a>
<FONT color="green">086</FONT>            for (int i = 0; i &lt; n; i++) {<a name="line.86"></a>
<FONT color="green">087</FONT>                h[i] = x[i + 1] - x[i];<a name="line.87"></a>
<FONT color="green">088</FONT>            }<a name="line.88"></a>
<FONT color="green">089</FONT>    <a name="line.89"></a>
<FONT color="green">090</FONT>            final double mu[] = new double[n];<a name="line.90"></a>
<FONT color="green">091</FONT>            final double z[] = new double[n + 1];<a name="line.91"></a>
<FONT color="green">092</FONT>            mu[0] = 0d;<a name="line.92"></a>
<FONT color="green">093</FONT>            z[0] = 0d;<a name="line.93"></a>
<FONT color="green">094</FONT>            double g = 0;<a name="line.94"></a>
<FONT color="green">095</FONT>            for (int i = 1; i &lt; n; i++) {<a name="line.95"></a>
<FONT color="green">096</FONT>                g = 2d * (x[i+1]  - x[i - 1]) - h[i - 1] * mu[i -1];<a name="line.96"></a>
<FONT color="green">097</FONT>                mu[i] = h[i] / g;<a name="line.97"></a>
<FONT color="green">098</FONT>                z[i] = (3d * (y[i + 1] * h[i - 1] - y[i] * (x[i + 1] - x[i - 1])+ y[i - 1] * h[i]) /<a name="line.98"></a>
<FONT color="green">099</FONT>                        (h[i - 1] * h[i]) - h[i - 1] * z[i - 1]) / g;<a name="line.99"></a>
<FONT color="green">100</FONT>            }<a name="line.100"></a>
<FONT color="green">101</FONT>    <a name="line.101"></a>
<FONT color="green">102</FONT>            // cubic spline coefficients --  b is linear, c quadratic, d is cubic (original y's are constants)<a name="line.102"></a>
<FONT color="green">103</FONT>            final double b[] = new double[n];<a name="line.103"></a>
<FONT color="green">104</FONT>            final double c[] = new double[n + 1];<a name="line.104"></a>
<FONT color="green">105</FONT>            final double d[] = new double[n];<a name="line.105"></a>
<FONT color="green">106</FONT>    <a name="line.106"></a>
<FONT color="green">107</FONT>            z[n] = 0d;<a name="line.107"></a>
<FONT color="green">108</FONT>            c[n] = 0d;<a name="line.108"></a>
<FONT color="green">109</FONT>    <a name="line.109"></a>
<FONT color="green">110</FONT>            for (int j = n -1; j &gt;=0; j--) {<a name="line.110"></a>
<FONT color="green">111</FONT>                c[j] = z[j] - mu[j] * c[j + 1];<a name="line.111"></a>
<FONT color="green">112</FONT>                b[j] = (y[j + 1] - y[j]) / h[j] - h[j] * (c[j + 1] + 2d * c[j]) / 3d;<a name="line.112"></a>
<FONT color="green">113</FONT>                d[j] = (c[j + 1] - c[j]) / (3d * h[j]);<a name="line.113"></a>
<FONT color="green">114</FONT>            }<a name="line.114"></a>
<FONT color="green">115</FONT>    <a name="line.115"></a>
<FONT color="green">116</FONT>            final PolynomialFunction polynomials[] = new PolynomialFunction[n];<a name="line.116"></a>
<FONT color="green">117</FONT>            final double coefficients[] = new double[4];<a name="line.117"></a>
<FONT color="green">118</FONT>            for (int i = 0; i &lt; n; i++) {<a name="line.118"></a>
<FONT color="green">119</FONT>                coefficients[0] = y[i];<a name="line.119"></a>
<FONT color="green">120</FONT>                coefficients[1] = b[i];<a name="line.120"></a>
<FONT color="green">121</FONT>                coefficients[2] = c[i];<a name="line.121"></a>
<FONT color="green">122</FONT>                coefficients[3] = d[i];<a name="line.122"></a>
<FONT color="green">123</FONT>                polynomials[i] = new PolynomialFunction(coefficients);<a name="line.123"></a>
<FONT color="green">124</FONT>            }<a name="line.124"></a>
<FONT color="green">125</FONT>    <a name="line.125"></a>
<FONT color="green">126</FONT>            return new PolynomialSplineFunction(x, polynomials);<a name="line.126"></a>
<FONT color="green">127</FONT>        }<a name="line.127"></a>
<FONT color="green">128</FONT>    }<a name="line.128"></a>




























































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